Debt, in essence, is an obligation to do something, generally to perform some type of work. In the mainstream, it has come to stand for “money that you have to pay”. But money only quantifies debt, similar to how temperature quantifies heat.
Debt can be non-financial. Software engineers use the term technical debt. It is created when you choose to write crappy code, because you need to save the day and don’t have enough time to make it perfect. When it accumulates so much so that it blocks the project, somebody—either you or some other unfortunate soul—will have to pay for it by fixing it. One of the most essential skills a sofware engineer can learn is to manage technical debt in a way that maximizes productivity and success.
The same pattern can be observed in psychology. It is human nature to repress emotions, memories and thoughts that we cannot deal with right now, for any reason. Whenever we do that, we incur emotional or mental debt. When it accumulates so much so that it starts hindering our life, we feel compelled to pay it by bringing our attention back to it. We then have to “process” it, which means to understand it, recontextualize it, put it in a different light, and so on. For someone who has been accumulating emotional debt their whole lives, paying it can be as difficult and confusing as paying tens of thousands of dollars in financial debt.
A friend of mine once told me that when he has a relatively bad experience with someone, he just erases the memory and forgets about them. The problem with that statement is that the brain does not have a delete() function. In the short term, the brain can recall a memory, reinterpret it, but cannot erase it, a traumatic one above all. So what he actually means is that he represses it. If you have ever met someone like that, you could safely assume that their subconscious is swarming with unprocessed emotions that influence their life without them being aware of it. An indicator of a crammed subconscious is experiencing the same problem again and again, with different people, in different places.